Not consistently—the more usual pattern is to use þ at the beginning of words and ð internally, even if the internal sound is voiceless.
In both languages, the two sounds are usually allophones and are perceived as the same sound influenced by context—the way the “th” sound in “breath” and “breathe” are perceived as the same consonant, just influenced by the preceding vowel. (If we wrote “breþ” and ‘breeð”, the different letters would hide the fact that we hear them as the same sound.)
Isn’t þ in Icelandic generally voiceless, as in ‘thin’ for example?
Not consistently—the more usual pattern is to use þ at the beginning of words and ð internally, even if the internal sound is voiceless.
In both languages, the two sounds are usually allophones and are perceived as the same sound influenced by context—the way the “th” sound in “breath” and “breathe” are perceived as the same consonant, just influenced by the preceding vowel. (If we wrote “breþ” and ‘breeð”, the different letters would hide the fact that we hear them as the same sound.)
I’d really like to see an example of a voiceless ð. I can’t think of one as a native speaker.
(You then get internal þ in compound words which we shan’t consider a contradiction)